Complete Theory

Worked Examples

Example 1ODE with complex roots

Example 2Particular solution (undetermined coefficients)

Example 3Variation of parameters

Example 4Resonance

Example 5Classifying a 2×2 system equilibrium

Exercise 1HomogeneousMedium

📋 Problem to solve

Solve

y''-3y'+2y=0

Exercise 2HomogeneousMedium

📋 Problem to solve

Solve

y''+2y'+5y=0

Exercise 3Variation of parametersHard

📋 Problem to solve

Solve

y''-y=e^x

via variation of parameters.

Exercise 4SystemsHard

📋 Problem to solve

Classify the equilibrium of

x'=x+y

y'=4x+y

Exercise 5ResonanceMedium

📋 Problem to solve

Solve

y''+y=\cos x

y(0)=0

y'(0)=1

Exercise 6Critical dampingMedium

📋 Problem to solve

Solve

y''+4y'+4y=0

and state the damping type.

Exercise 7SystemsHard

📋 Problem to solve

Classify the equilibrium of

\mathbf{x}'=\begin{pmatrix}0&-1\\1&0\end{pmatrix}\mathbf{x}

📚

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